How man 4 letter code words can be made using the letters in the word pencil if repetitions are permitted?
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To find the number of 4-letter code words that can be made using the letters in the word "pencil" with repetitions permitted, you can use the concept of permutations with repetition.
Permutations with repetition refer to arrangements where some objects are repeated. In this case, each letter in the word "pencil" can be repeated since repetitions are permitted.
To calculate the number of permutations with repetition, you can use the following formula:
n^r
Where:
- n is the number of options for each slot, which in this case is the number of letters in the word "pencil" (6)
- r is the number of slots to fill, which in this case is 4
So, using the formula, substituting the values, the calculation becomes:
6^4 = 6 * 6 * 6 * 6 = 1,296
Therefore, there are 1,296 possible 4-letter code words that can be made using the letters in the word "pencil" when repetitions are permitted.